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Lời giải:
\(P(x)=x(x+2)(x+3)(x+5)-7\)
\(=[x(x+5)][(x+2)(x+3)]-7\)
\(=(x^2+5x)(x^2+5x+6)-7\)
\(=a(a+6)-7\) (đặt \(x^2+5x=a\) )
\(=a^2+6a-7=a^2-a+7a-7\)
\(=a(a-1)+7(a-1)=(a-1)(a+7)\)
\(=(x^2+5x-1)(x^2+5x+7)\)
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\(Q(x)=(4x-2)(10x+4)(5x+7)(2x+1)+17\)
\(=4(2x-1)(5x+2)(5x+7)(2x+1)+17\)
\(=4[(2x-1)(5x+7)][(5x+2)(2x+1)]+17\)
\(=4(10x^2+9x-7)(10x^2+9x+2)+17\)
\(=4a(a+9)+17\) (đặt \(10x^2+9x-7=a\)
\(=4a^2+36a+17=(2a+9)^2-8^2\)
\(=(2a+9-8)(2a+9+8)=(2a+1)(2a+17)\)
\(=(20x^2+18x-13)(20x^2+18x+3)\)
\(R(x)=(3x+2)(3x-5)(x-1)(9x+10)+24x^2\)
\(=[(3x+2)(3x-5)][(x-1)(9x+10)]+24x^2\)
\(=(9x^2-9x-10)(9x^2+x-10)+24x^2\)
\(=(a-9x)(a+x)+24x^2\) (đặt \(9x^2-10=a\) )
\(=a^2-8ax+15x^2=(a^2-5ax)-(3ax-15x^2)\)
\(=a(a-5x)-3x(a-5x)=(a-3x)(a-5x)\)
\(=(9x^2-3x-10)(9x^2-5x-10)\)
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\(H(x)=(x-18)(x-7)(x+35)(x+90)-67x^2\)
\(=[(x-18)(x+35)][(x-7)(x+90)]-67x^2\)
\(=(x^2+17x-630)(x^2+83x-630)-67x^2\)
\(=a(a+66x)-67x^2\) (đặt \(x^2+17x-630=a\) )
\(=a^2-ax+67ax-67x^2\)
\(=a(a-x)+67x(a-x)=(a-x)(a+67x)\)
\(=(x^2+16x-630)(x^2+84x-630)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a) Đặt t = x2
bthuc <=> t2 - 7t + 16
Từ đây ta không thể phân tích được :)
b) x3 - 2x2 + 5x - 4
= x3 - x2 - x2 + x + 4x - 4
= x2( x - 1 ) - x( x - 1 ) + 4( x - 1 )
= ( x - 1 )( x2 - x + 4 )
c) x3 - 2x2 + x - 3 ( phân tích hổng ra :)) )
d) 3x3 - 4x2 + 12x - 4 ( phân tích hổng ra p2 :)) )
e) 6x3 + x2 + x + 1
= 6x3 + 3x2 - 2x2 - x + 2x + 1
= 3x2( 2x + 1 ) - x( 2x - 1 ) + ( 2x + 1 )
= ( 2x + 1 )( 3x2 - x + 1 )
f) 4x3 + 6x2 + 4x + 1
= 4x3 + 2x2 + 4x2 + 2x + 2x + 1
= 2x2( 2x + 1 ) + 2x( 2x + 1 ) + ( 2x + 1 )
= ( 2x + 1 )( 2x2 + 2x + 1 )
a) x3 + 2x - 3
=x3+x2+3x-x2+x+3
=x(x2+x+3)-1(x2+x+3)
=(x-1)(x2+x+3)
b) x3 - x2 + x + 3
=x3-2x2+3x+x2-2x+3
=x(x2-2x+3)+1(x2-2x+3)
=(x+1)(x2-2x+3)
c) 3x3 - 4x2 + 13x - 4
=3x3-3x2+12-x2-x+4
=3x(x2-x+4)-1(x2-x+4)
=(3x-1)(x2-x+4)
d) 6x3 + x2 + x + 1
=6x3-2x2+2x+3x2-x+1
=2x(3x2-x+1)+1(3x2-x+1)
=(2x+1)(3x2-x+1)
e)bạn phân tích tương tự nhé mk cho đáp án để bạn đổi chiếu nè
=(2x+1)(2x2+2x+1)
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
a) 4x2 - 12x + 5
= 4x2 - 2x - 10x + 5
= (4x2 - 2x) + (-10x + 5)
= 2x(x - 2) - 5 ( x - 2)
= (x - 2) (2x - 5)
còn lại tương tự nha
ok mk nha!!! 5547565876876876345645645666575676575688768898778978234532344543
ý lộn mk làm lại:
4x2 - 12x + 5
= 4x2 - 2x - 10x + 5
= 2x(2x - 1) - 5(2x - 1)
= (2x - 1) (2x - 5)
ok mk nhé!!!! 546465765876876876769789785653645645234634634457756756
a)
\((6x+5)^2(3x+2)(x+1)-35\)
\(=(36x^2+60x+25)(3x^2+5x+2)-35\)
\(=[12(3x^2+5x+2)+1](3x^2+5x+2)-35\)
\(=(12a+1)a-35=12a^2+a-35\) (đặt \(3x^2+5x+2=a)\)
\(=4a(3a-5)+7(3a-5)=(4a+7)(3a-5)\)
\(=(12x^2+20x+15)(9x^2+15x+1)\)
b)
\(8(4x+1)(2x-3)(4x-3)(x+1)-130\)
\(=8[(4x+1)(4x-3)][(2x-3)(x+1)]-130\)
\(=8(16x^2-8x-3)(2x^2-x-3)-130\)
\(=8(8a+21)a-130\) (Đặt \(2x^2-x-3=a\) )
\(=64a^2+168a-130=2(8a-5)(4a+13)\)
\(=2(8x^2-4x+1)(16x^2-8x-29)\)
c)
\((4x+1)(12x-1)(3x+2)(x+1)-4\)
\(=[(4x+1)(3x+2)][(12x-1)(x+1)]-4\)
\(=(12x^2+11x+2)(12x^2+11x-1)-4\)
\(=(a+2)(a-1)-4\) (đặt \(a=12x^2+11x\) )
\(=a^2+a-6=(a-2)(a+3)\)
\(=(12x^2+11x-2)(12x^2+11x+3)\)
d)
\((x+2)(x+3)^2(x+4)-12\)
\(=[(x+2)(x+4)](x+3)^2-12\)
\(=(x^2+6x+8)(x^2+6x+9)-12\)
\(=a(a+1)-12\) (Đặt \(x^2+6x+8=a\) )
\(=a^2+a-12=(a-3)(a+4)=(x^2+6x+5)(x^2+6x+12)\)
\(=(x+1)(x+5)(x^2+6x+12)\)